The Net, The EU and The UN
The reasoning is that if one country controls the net, they could shut others out of it. So instead of the US running the net (which we invented, and spread) a UN committee, with Iran, Cuba and China pushing for membership, would decide who gets what address blocks. Now think about your news in the last month. China is cracking down, asking Microsloth for new filtering software to censor content. They've asked Yahoo! to turn over records of use by disadents. Cuba doesn't allow most of it's folks on the net, and Iran is more restrictive than China.
These are the folks we should let run the net?
To China, the EU, et. al. FUCK OFF! The US developed, built and allowed the internet to spread, and it's works quite well. If you are so worried about bandwidth and folks being locked out, develop another that you control. You can even let it work with the existing one, I'm sure a few first year IT students could explain how translation tables could be worked to merge two networks with identical ID's on each (not easy, but not impossible). China could build their own, too.
The fact is, the UN can't manage the remodeling of it's offices (5 years behind, 300% over budget) what makes them think they could handle something complex? And why do they think the US will just hand over the keys to the Domain Name Servers?